On the equivalence of case-crossover and time series methods in environmental epidemiology

Biostatistics. 2007 Apr;8(2):337-44. doi: 10.1093/biostatistics/kxl013. Epub 2006 Jun 29.


The case-crossover design was introduced in epidemiology 15 years ago as a method for studying the effects of a risk factor on a health event using only cases. The idea is to compare a case's exposure immediately prior to or during the case-defining event with that same person's exposure at otherwise similar "reference" times. An alternative approach to the analysis of daily exposure and case-only data is time series analysis. Here, log-linear regression models express the expected total number of events on each day as a function of the exposure level and potential confounding variables. In time series analyses of air pollution, smooth functions of time and weather are the main confounders. Time series and case-crossover methods are often viewed as competing methods. In this paper, we show that case-crossover using conditional logistic regression is a special case of time series analysis when there is a common exposure such as in air pollution studies. This equivalence provides computational convenience for case-crossover analyses and a better understanding of time series models. Time series log-linear regression accounts for overdispersion of the Poisson variance, while case-crossover analyses typically do not. This equivalence also permits model checking for case-crossover data using standard log-linear model diagnostics.

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Air Pollution*
  • Cross-Over Studies*
  • Environmental Exposure*
  • Epidemiologic Methods*
  • Humans
  • Logistic Models*